That's the key question for this story I wrote for Moving Image Source: "The Vanishing: The demise of VHS, and the movies disappearing along with it."
The number of classic movies and auteur films available only in the quickly dying format of VHS is too numerous to mention, but here's a sampling from my research:
"Greed" (Erich von Stroheim), "Underworld U.S.A." (Sam Fuller), "State of Siege" (Costas Gavras), "Providence" (Alain Resnais), "Story of the Last Chrysanthemums" (Kenji Mizoguchi), "I Only Want You to Love Me" (Rainer Fassbinder), "Where Is the Friend's House?" (Abbas Kiarostami), "Antonio Das Mortes" (Glauber Rocha), "Cruel Story of Youth" (Nagisa Oshima), "Marianne and Julianne" (Margarethe Von Trotta), "The Mortal Storm" (Frank Borzage), "The Mother and the Whore" (Jean Eustache).
In the past, if these films never made it to DVD, it simply would be a disappointment. But now it's a tragedy. With videostores shutting down right and left, many removing their VHS stock and VHS players themselves relics of a bygone era, replaced by a shiny, new all-digital future, many of these films will be left behind. As critic Dave Kehr explained to me in the piece: The studios "don’t have any idea what they've got in their library. They were releasing a number of films on VHS that you can’t get in any form today." In the switch from VHS to DVD, he explains, "we lost a tremendous amount of stuff, because they had to remaster them and no one wanted to spend the money."
And if the topic interests you, be sure to check out Mike Atkinson's (more optimistic) companion piece, "Ashes of Time", which suggests downloadable DVD-R bootlegs as our last best option.